Chapter 4: Individual and Market Demand
I
F
I
C
Formatted: Bullets and Numbering
3. Jane always gets twice as much utility from an extra ballet ticket as she does from an extra basketball
ticket, regardless of how many tickets of either type she has. Draw Jane’s income consumption curve and her
Engel curve for ballet tickets.
Jane will consume either all ballet tickets or all basketball tickets, depending on the two prices.
As long as ballet tickets are less than twice the price of basketball tickets, she will choose all
ballet. If ballet tickets are more than twice the price of basketball tickets then she will choose all
basketball. This can be determined by comparing the marginal utility per dollar for each type of
ticket, where her marginal utility of another ballet ticket is 2 and her marginal utility of another
basketball ticket is 1. Her income consumption curve will then lie along the axis of the good that
she chooses. As income increases, and the budget line shifts out, she will stick with the chosen
good. The Engel curve is a linear, upward-sloping line. For any given increase in income, she
will be able to purchase a fixed amount of extra tickets.
4. a. Orange juice and apple juice are known to be perfect substitutes. Draw the appropriate price-
consumption (for a variable price of orange juice) and income-consumption curves.
We know that the indifference curves for perfect substitutes will be straight lines. In this case, the
consumer will always purchase the cheaper of the two goods. If the price of orange juice is less than
43

Chapter 4: Individual and Market Demand
that of apple juice, the consumer will purchase only orange juice and the price consumption curve
will be on the “orange juice axis” of the graph (point F). If apple juice is cheaper, the consumer will
purchase only apple juice and the price consumption curve will be on the “apple juice axis” (point
E). If the two goods have the same price, the consumer will be indifferent between the two; the price
consumption curve will coincide with the indifference curve (between E and F). See the figure
below.
Apple J u ice
PA < PO
PA = PO
E
PA > PO
U
F
Or a n ge J u ice
Assuming that the price of orange juice is less than the price of apple juice, the consumer will
maximize her utility by consuming only orange juice. As the level of income varies, only the
amount of orange juice varies. Thus, the income consumption curve will be the “orange juice axis”
in the figure below.
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Chapter 4: Individual and Market Demand
Apple J u ice
Bu dget
Con st r a in t
In come
Con su mpt ion
Cu rve
U3
U2
U1
Or a n ge J u ice
4.b. Left shoes and right shoes are perfect complements. Draw the appropriate price-consumption and income-
consumption curves.
For goods that are perfect complements, such as right shoes and left shoes, we know that the
indifference curves are L-shaped. The point of utility maximization occurs when the budget
constraints, L1 and L2 touch the kink of U1 and U2. See the following figure.
Righ t
Sh oes
P r ice
Con su mpt ion
Cur ve
U2
U1
L1 L2
Left Shoes
In the case of perfect complements, the income consumption curve is also a line through the corners
of the L-shaped indifference curves. See the figure below.
45

Chapter 4: Individual and Market Demand
Bill’s utility fell between weeks 1 and 2 since he ended up with less of both goods. In week 2, the
price of good 1 rose and his income remained constant. The budget line will pivot inwards and he
will have to move to a lower indifference curve. Between week 1 and week 3 his utility rose. The
increase in income more than compensated him for the rise in the price of good 1. Since the price
of good 1 rose by $1, he would need an extra $10 to afford the same bundle of goods that he chose
in week 1. This can be found by multiplying week 1 quantities times week 2 prices. However, his
income went up by $15, so his budget line shifted out beyond his week 1 bundle. Therefore, his
original bundle lies within his new budget set, and his new week 3 bundle is on a higher
indifference curve.
b. Now consider the following information about the choices that Mary makes:
x1 x2 P1 P2 I
Formatted: Space Before: 1.2 line,
After: 1.2 line, Line spacing: 1.5
lines
Week 1 10 20 2 1 40
Formatted: Space Before: 1.2 line,
After: 1.2 line, Line spacing: 1.5
lines
Week 2 6 14 2 2 40
Formatted: Space Before: 1.2 line,
After: 1.2 line, Line spacing: 1.5
lines
Week 3 20 10 2 2 60
Formatted: Space Before: 1.2 line,
After: 1.2 line, Line spacing: 1.5
lines
Did Mary’s utility increase or decrease between week 1 and week 3? Does Mary consider both goods
to be normal goods? Explain.
Mary’s utility went up. To afford the week 1 bundle at the new prices, she would need an extra
$20, which is exactly what happened to her income. However, since she could have chosen the
original bundle at the new prices and income but chose not to, she must have found a bundle that
left her slightly better off. In the graph below, the week 1 bundle is at the intersection of the week
1 and week 3 budget lines. The week 3 bundle is somewhere on the line segment that lies above
the week 1 indifference curve. This bundle will be on a higher indifference curve. A good is
normal if more is chosen when income increases. Good 2 is not normal because when her income
went up from week 2 to week 3, she consumed less of the good (holding prices the same).
47

Chapter 4: Individual and Market Demand
good 2
week 1 bundle
week 3 bundle
good 1
c. Finally, examine the following information about Jane’s choices:
x1 x2 P1 P2 I
Formatted: Space Before: 1.2 line,
After: 1.2 line, Line spacing: 1.5
lines
Week 1 12 24 2 1 48
Formatted: Space Before: 1.2 line,
After: 1.2 line, Line spacing: 1.5
lines
Week 2 16 32 1 1 48
Formatted: Space Before: 1.2 line,
After: 1.2 line, Line spacing: 1.5
lines
Week 3 12 24 1 1 36
Formatted: Space Before: 1.2 line,
After: 1.2 line, Line spacing: 1.5
lines
Draw a budget line, indifference curve graph that illustrates Jane’s three chosen bundles. What can
you say about Jane’s preferences in this case? Identify the income and substitution effects that result
from a change in the price of good 1.
In week 2, the price of good 1 goes down and Jane consumes more of both goods. Her budget line
pivots outwards. In week 3 the prices remain at the new level, but Jane’s income is reduced. This
will shift her budget line inwards, and cause her to consume less of both goods. Notice that Jane
always consumes the two goods in a fixed 1:2 ratio. This means that Jane views the two goods as
perfect complements, and her indifference curves are L-shaped. Intuitively if the two goods are
complements, there is no reason to substitute one for the other during a price change because they
have to be consumed in a set ratio. Thus the substitution effect will be zero. When the price ratio
48

Chapter 4: Individual and Market Demand
changes and utility is kept at the same level, Jane will choose the same point (12,24). The income
effect causes her to buy 4 more units of good 1 and 8 more units of good 2.
good 2 week 1 a nd 3
bund le
week 2
bund le
good 1
6. Two individuals, Sam and Barb, derive utility from the hours of leisure (L) they consume and from the
amount of goods (G) they consume. In order to maximize utility they need to allocate the 24 hours in the day
between leisure hours and work hours. Assume that all hours not spent working are leisure hours. The price
of a good is equal to $1 and the price of leisure is equal to the hourly wage. We observe the following
information about the choices that the two individuals make:
Sam Barb Sam Barb
Formatted: Space Before: 1.2 line,
After: 1.2 line, Line spacing: 1.5
lines
Price of G Price of L L(hours) L(hours) G($) G($)
Formatted: Space Before: 1.2 line,
After: 1.2 line, Line spacing: 1.5
lines
1 8 16 14 64 80
Formatted: Space Before: 1.2 line,
After: 1.2 line, Line spacing: 1.5
lines
1 9 15 14 81 90
Formatted: Space Before: 1.2 line,
After: 1.2 line, Line spacing: 1.5
lines
1 10 14 15 100 90
Formatted: Space Before: 1.2 line,
After: 1.2 line, Line spacing: 1.5
lines
1 11 14 16 110 88
Formatted: Space Before: 1.2 line,
After: 1.2 line, Line spacing: 1.5
lines
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Chapter 4: Individual and Market Demand
Graphically illustrate Sam’s leisure demand curve and Barb’s leisure demand curve. Place price on the
vertical axis and leisure on the horizontal axis. Given that they both maximize utility, how can you explain
the difference in their leisure demand curves?
It is important to remember that less leisure implies more hours spent working at the higher wage.
Sam’s leisure demand curve is downward sloping. As the price of leisure (the wage) rises, he
chooses to consume less leisure to spend more time working at a higher wage to buy more goods.
Barb’s leisure demand curve is upward sloping. As the price of leisure rises, she chooses to
consume more leisure since her working hours are generating more income. This difference in
demand can be explained by examining the income and substitution effects for the two
individuals. The substitution effect measures the effect of the change in the price of leisure,
keeping utility constant (the budget line will rotate around the current indifference curve). Since
the substitution effect is always negative, a rise in the price of leisure will cause both individuals
to consume less leisure. The income effect measures the change in purchasing power caused by
the change in the price of leisure. Here, when the price of leisure (the wage) rises, there is an
increase in purchasing power (the new budget line will shift outwards). Assuming both
individuals consider leisure to be a normal good (this is not a necessary assumption for Sam), then
the increase in purchasing power will increase demand for leisure. For Sam, the reduction in
leisure demand caused by the substitution effect outweighs the increase in demand for leisure
caused by the income effect. For Barb, her income effect is larger than her substitution effect.
Formatted: Bullets and Numbering
7. The director of a theatre company in a small college town is considering changing the way he prices
tickets. He has hired an economic consulting firm to estimate the demand for tickets. The firm has classified
people who go the theatre into two groups, and has come up with two demand functions. The demand curves
for the general public ( Qgp ) and students ( Qs ) are given below.
Qgp = 500 − 5P
Qs = 200 − 4P
a. Graph the two demand curves on one graph, with P on the vertical axis and Q on the horizontal axis.
If the current price of tickets is $35, identify the quantity demanded by each group.
Both demand curves are downward sloping and linear. For the general public, the vertical
intercept is 100 and the horizontal intercept is 500. For the students, the vertical intercept is 50
and the horizontal intercept is 200. The general public demands
Qgp = 500 − 5(35) = 325 tickets and the students demand Qs = 200 − 4(35) = 60 tickets.
b. Find the price elasticity of demand for each group at the current price and quantity.
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Chapter 4: Individual and Market Demand
−5(35)
The elasticity for the general public is εgp = = −0.54 and the elasticity for the students
325
−4(35)
is εgp = = −2.33 . If the price of tickets increases by one percent then the general
60
public will demand .54% fewer tickets and the students will demand 2.33% fewer tickets.
c. Is the director maximizing the revenue he collects from ticket sales by charging $35 for each ticket?
Explain.
No he is not maximizing revenue since neither one of the calculated elasticities is equal to –1.
Since demand by the general public is inelastic at the current price, the director could increase the
price and quantity demanded would fall by a smaller amount in percentage terms, causing revenue
to increase. Since demand by the students is elastic at the current price, the director could
decrease the price and quantity demanded would increase by a larger amount in percentage terms,
causing revenue to increase.
d. What price should he charge each group if he wants to maximize revenue collected from ticket sales?
To figure this out, find the formula for elasticity, set it equal to –1, and solve for price and
quantity. For the general public:
−5P
εgp = = −1
Q
5P = Q = 500 − 5P
P = 50
Q = 250.
For the students:
−4P
εs = = −1
Q
4P = Q = 200 − 4P
P = 25
Q = 100.
8. Judy has decided to allocate exactly $500 to textbooks at college every year, even though she knows that
the prices are likely to increase by 5 to 10 percent per year and that she will be getting a substantial monetary
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Chapter 4: Individual and Market Demand
gift from her grandparents next year. What is Judy’s price elasticity of demand for textbooks? Income
elasticity?
Price elasticity of demand is percentage change in quantity for a given percentage change in price.
Judy knows that prices will go up in the future. Given she is going to spend a fixed amount on
books, this must mean that her quantity demanded will decrease as price increases. Since
expenditure is constant the percentage change in quantity demanded must be equal to the
percentage change in price, and price elasticity is -1. Income elasticity must be zero because
although she expects a large monetary gift, she has no plans to purchase more books. Recall that
income elasticity is defined as the percentage change in quantity demanded for a given percentage
change in income, all else the same.
9. The ACME Corporation determines that at current prices the demand for its computer chips has a price
elasticity of -2 in the short run, while the price elasticity for its disk drives is -1.
a. If the corporation decides to raise the price of both products by 10 percent, what will happen to its
sales? To its sales revenue?
We know the formula for the elasticity of demand is:
%ΔQ
EP = .
%ΔP
For computer chips, EP = -2, so a 10 percent increase in price will reduce the quantity sold by 20
percent. For disk drives, EP = -1, so a 10 percent increase in price will reduce sales by 10 percent.
Sales revenue is equal to price times quantity sold. Let TR1 = P1Q1 be revenue before the price
change and TR2 = P2Q2 be revenue after the price change.
For computer chips:
ΔTRcc = P2Q2 - P1Q1
ΔTRcc = (1.1P1 )(0.8Q1 ) - P1Q1 = -0.12P1Q1, or a 12 percent decline.
For disk drives:
ΔTRdd = P2Q2 - P1Q1
ΔTRdd = (1.1P1 )(0.9Q1 ) - P1Q1 = -0.01P1Q1, or a 1 percent decline.
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Chapter 4: Individual and Market Demand
Therefore, sales revenue from computer chips decreases substantially, -12 percent, while the sales
revenue from disk drives is almost unchanged, -1 percent. Note that at the point on the demand
curve where demand is unit elastic, total revenue is maximized.
b. Can you tell from the available information which product will generate the most revenue for the firm?
If yes, why? If not, what additional information do you need?
No. Although we know the responsiveness of demand to changes in price, we need to know both
quantities and prices of the products to determine total sales revenue.
10. By observing an individual’s behavior in the situations outlined below, determine the relevant income
elasticities of demand for each good (i.e., whether the good is normal or inferior). If you cannot determine the
income elasticity, what additional information might you need?
a. Bill spends all his income on books and coffee. He finds $20 while rummaging through a used
paperback bin at the bookstore. He immediately buys a new hardcover book of poetry.
Books are a normal good since his consumption of books increases with income. Coffee is a normal
or neutral good since consumption of coffee did not fall when income increased.
b. Bill loses $10 he was going to use to buy a double espresso. He decides to sell his new book at a
discount to his friend and use the money to buy coffee.
Coffee is clearly a normal good.
c. Being bohemian becomes the latest teen fad. As a result, coffee and book prices rise by 25 percent.
Bill lowers his consumption of both goods by the same percentage.
Books and coffee are both normal goods since his response to a decline in real income is to decrease
consumption of both goods.
d. Bill drops out of art school and gets an M.B.A. instead. He stops reading books and drinking coffee.
Now he reads The Wall Street Journal and drinks bottled mineral water.
His tastes have changed completely, and we do not know exactly how he would respond to price and
income changes. We need more information regarding his new level of income, and relative prices
of the goods to determine the income elasticities.
11. Suppose the income elasticity of demand for food is 0.5, and the price elasticity of demand is –1.0.
Suppose also that Felicia spends $10,000 a year on food, the price of food is $2, and her income is $25,000.
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Chapter 4: Individual and Market Demand
a. If a sales tax on food were to cause the price of food to increase to $2.50, what would happen
to her consumption of food? (Hint: Since a large price change is involved, you should
assume that the price elasticity measures an arc elasticity, rather than a point elasticity.)
The price of food increases from $2 to $2.50, so arc elasticity should be used:
⎛ P1 + P2 ⎞
EP = ⎛ ΔQ ⎞ ⎜ 2 ⎟ .
⎝ ΔP ⎠ ⎜ Q1 + Q2 ⎟
⎜ ⎟
⎝ 2 ⎠
We know that EP = -1, P = 2, ΔP = 0.5, and Q=5000. We also know that Q2, the new quantity, is
Q + Δ Q. Thus, if there is no change in income, we may solve for ΔQ:
⎛ 2 + 2.5 ⎞
⎛ ΔQ⎞ ⎜ 2 ⎟
−1=
⎝ 0.5 ⎠ ⎜ 5,000 + (5,000 + ΔQ) ⎟
.
⎜ ⎟
⎝ 2 ⎠
By cross-multiplying and rearranging terms, we find that ΔQ = -1,000. This means that she
decreases her consumption of food from 5,000 to 4,000 units.
b. Suppose that she is given a tax rebate of $2,500 to ease the effect of the sales tax. What
would her consumption of food be now?
A tax rebate of $2,500 implies an income increase of $2,500. To calculate the response of demand to
the tax rebate, use the definition of the arc elasticity of income.
⎛ I1 + I2 ⎞
⎛ ΔQ⎞ ⎜ 2 ⎟.
EI =
⎝ ΔI ⎠ ⎜ Q1 + Q2 ⎟
⎜ ⎟
⎝ 2 ⎠
We know that EI = 0.5, I = 25,000, ΔI = 2,500, Q = 4,000 (from the answer to 11.a). Assuming no
change in price, we solve for ΔQ.
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Chapter 4: Individual and Market Demand
⎛ 25,000 + 27,500 ⎞
⎛ ΔQ ⎞ ⎜ 2 ⎟
0.5 = ⎜ ⎟
⎝ 2,500 ⎠ ⎜ 4,000 + (4,000 + ΔQ) ⎟
.
⎜ ⎟
⎝ 2 ⎠
By cross-multiplying and rearranging terms, we find that ΔQ = 195 (approximately). This means
that she increases her consumption of food from 4,000 to 4,195 units.
c. Is she better or worse off when given a rebate equal to the sales tax payments? Draw a
graph and explain.
Felicia is likely to be better off after the rebate. The amount of the rebate is enough to allow her to
purchase her original bundle of food and other goods. Recall that originally she consumed 5000
units of food. When the price went up by fifty cents per unit, she needed an extra
5000*$0.50=$2,500 to afford the same quantity of food without reducing the quantity of the other
goods consumed. This is the exact amount of the rebate. However, she did not choose to return to
her original bundle. We can therefore infer that she found a better bundle that gave her a higher
level of utility. In the graph below, when the price of food increases, the budget line will pivot
inwards. When the rebate is given, this new budget line will shift outwards. The bundle after the
rebate is on that part of the new budget line that was previously unaffordable, and that lies above
the original indifference curve.
other good
bundle after rebate
original bundle
food
Formatted: Bullets and Numbering
12. You run a small business and would like to predict what will happen to the quantity demanded for your
product if you raise your price. While you do not know the exact demand curve for your product, you do
know that in the first year you charged a price of $45 and sold 1200 units and in the second year you charged
a price of $30 and sold 1800 units.
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Chapter 4: Individual and Market Demand
a. If you plan to raise your price by 10% what would be a reasonable estimate of what might
happen to quantity demanded in percentage terms?
To answer this question, you need to find the elasticity. You can estimate the slope of the demand
curve in the following way:
∂Q ΔQ 1200 − 1800 600
= = = = −40 .
∂P ΔP 45 − 30 −15
You can now use the elasticity formula and calculate elasticity at each data point, as well as the
average point. The elasticities are:
P ΔQ −40(45)
P=45 and Q=1200 elasticity= = = −1.5.
Q ΔP 1200
P ΔQ −40(30)
P=30 and Q=1800 elasticity== = = −0.67.
Q ΔP 1800
P ΔQ −40(37.5)
P=37.5 and Q=1500 elasticity== = = −1.
Q ΔP 1500
Given you are coming up with an estimate based on only two data points, it may be best to go with
the average point. If elasticity is -1 then a 10% increase in price will cause quantity demanded to
fall by 10%.
b. If you raise your price by 10%, will revenue increase or decrease?
If elasticity is really -1 then revenue will fall if price is increased. If elasticity is actually closer to
-0.67 (inelastic) then revenue will rise because the effect of the increase in price will outweigh the
effect of the decrease in quantity. If elasticity is closer to -1.5 (elastic) then revenue will fall when
price is increased.
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Chapter 4: Individual and Market Demand
13. Suppose you are in charge of a toll bridge that costs essentially nothing to operate. The demand for
1
bridge crossings Q is given by P = 15 − Q.
2
a. Draw the demand curve for bridge crossings.
The demand curve is linear and downward sloping. The vertical intercept is 15 and the horizontal
intercept is 30.
b. How many people would cross the bridge if there were no toll?
At a price of zero, the quantity demanded would be 30.
c. What is the loss of consumer surplus associated with a bridge toll of $5?
If the toll is $5 then the quantity demanded is 20. The lost consumer surplus is the area below the
price line of $5 and to the left of the demand curve. The lost consumer surplus can be calculated
as (5*20)+0.5(5*10)=$125.
a. The toll bridge operator is considering an increase in the toll to $7. At this new higher price,
how many people would cross the bridge? Would the toll bridge revenue increase or
decrease? What does your answer tell you about the elasticity of demand?
At a toll of $7, the quantity demanded would be 16. The initial toll revenue was $5*20=$100.
The new toll revenue is $7*16=$112. Since the revenue went up when the toll was increased,
demand is inelastic (the increase in price (40%) outweighed the decline in quantity demanded
(20%)).
b. Find the lost consumer surplus associated with the increase in the price of the toll from $5 to
$7.
The lost consumer surplus is (7-5)*16+0.5(7-5)(20-16)=$36.
14. Vera has decided to upgrade the operating system on her new PC. She hears that the new Linux
operating system is technologically superior to the Windows operating system and substantially lower in
price. However, when she asks her friends it turns out they all use PCs with Windows. They agree that
Linux is more appealing but add that they see relatively few copies of Linux on sale at the local retail software
stores. Based on what she learns and observes, Vera chooses to upgrade her PC with Windows. Can you
explain her decision?
Vera is consuming under the influence of a positive network externality (not a bandwagon effect).
When she hears that there are limited software choices that are compatible with the Linux operating
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Chapter 4: Individual and Market Demand
system, she decides to go with Windows. If she had not been interested in acquiring much software,
she may have gone with Linux. See Example 4.6 in the text. In the future, however, there may be a
bandwagon effect, i.e., the purchase of Linux because almost everyone else has it. As more people
use Linux, manufacturers might introduce more software that is compatible with the Linux operating
system. As the Linux based software section at the local computer store gets larger and larger, this
prompts more consumers to purchase Linux. Eventually, the Windows section shrinks as the Linux
section becomes larger and larger.
16. Suppose that you are the consultant to an agricultural cooperative that is deciding whether members
should cut their production of cotton in half next year. The cooperative wants your advice as to whether this
will increase the farmers’ revenues. Knowing that cotton (C) and watermelons (W) both compete for
agricultural land in the South, you estimate the demand for cotton to be C=3.5-1.0PC+0.25PW+0.50I, where PC
is the price of cotton, PW the price of watermelon, and I income. Should you support or oppose the plan? Is
there any additional information that would help you to provide a definitive answer?
Formatted: Normal, Justified,
If production of cotton is cut in half, then the price of cotton will increase, given that we see from the
Indent: Left: 36 pt, Right: 36 pt,
equation above that demand is downward sloping. With price increasing and quantity demanded Space Before: 1.2 line, After: 1.2
line, Line spacing: 1.5 lines, Don't
decreasing, revenue could go either way. It depends on whether demand is inelastic or elastic at the hyphenate, Tabs: -36 pt, Left + 0
pt, Left
current price. If demand is inelastic then a decrease in production and an increase in price could
increase revenue. If demand is elastic then a decrease in production and an increase in price will
clearly decrease revenue. You need to know the current price and/or quantity demanded to figure Deleted: ¶
¶
out the current level of elasticity.
58